Time series Forecasting using svm

Time series Forecasting using svm

• 1.
  Financial time seriesforecasting using support vector machines Author: Kyoung-jae Kim 2003 Elsevier B.V.
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  Outline • • • • Introduction to SVM Introductionto datasets Experimental settings Analysis of experimental results
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  Linear separability • Linearseparability – In general, two groups are linearly separable in ndimensional space if they can be separated by an (n − 1)-dimensional hyperplane.
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  Support Vector Machines •Maximum-margin hyperplane maximum-margin hyperplane
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  Formalization • Training data •Hyperplane • Parallel bounding hyperplanes
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  Objective • Minimize (inw, b) ||w|| • subject to (for any i=1, …, n)
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  A 2-D case •In 2-D: – Training data: xi ci <1, 1> 1 <2, 2> 1 <2, 1> -1 <3, 2> -1 -2x+2y+1=1 -2x+2y+1=0 -2x+2y+1=-1 w=<-2, 2> b=-1 margin=sqrt(2)/2
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  Not linear separable •No hyperplane can separate the two groups
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  Soft Margin • Choosea hyperplane that splits the examples as cleanly as possible • Still maximizing the distance to the nearest cleanly split examples • Introduce an error cost C d*C
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  Higher dimensions • Separationmight be easier
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  Kernel Trick • Buildmaximal margin hyperplanes in highdimenisonal feature space depends on inner product: more cost • Use a kernel function that lives in low dimensions, but behaves like an inner product in high dimensions
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  Kernels • Polynomial – K(p,q) = (p•q + c)d • Radial basis function – K(p, q) = exp(-γ||p-q||2) • Gaussian radial basis – K(p, q) = exp(-||p-q||2/2δ2)
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  Tuning parameters • Errorweight –C • Kernel parameters – δ2 –d – c0
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  Underfitting & Overfitting •Underfitting • Overfitting • High generalization ability
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  Datasets • Input variables –12 technical indicators • Target attribute – Korea composite stock price index (KOSPI) • 2928 trading days – 80% for training, 20% for holdout
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  Settings (1/3) • SVM –kernels • polynomial kernel • Gaussian radial basis function – δ2 – error cost C
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  Settings (2/3) • BP-Network –layers • 3 – number of hidden nodes • 6, 12, 24 – learning epochs per training example • 50, 100, 200 – learning rate • 0.1 – momentum • 0.1 – input nodes • 12
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  Settings (3/3) • Case-BasedReasoning – k-NN • k = 1, 2, 3, 4, 5 – distance evaluation • Euclidean distance
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  Experimental results • Theresults of SVMs with various C where δ2 is fixed at 25 • Too small C • underfitting* • Too large C • overfitting* * F.E.H. Tay, L. Cao, Application of support vector machines in -nancial time series forecasting, Omega 29 (2001) 309–317
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  Experimental results • Theresults of SVMs with various δ2 where C is fixed at 78 • Small value of δ2 • overfitting* • Large value of δ2 • underfitting* * F.E.H. Tay, L. Cao, Application of support vector machines in -nancial time series forecasting, Omega 29 (2001) 309–317
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  Experimental results andconclusion • SVM outperformes BPN and CBR • SVM minimizes structural risk • SVM provides a promising alternative for financial time-series forecasting • Issues – parameter tuning